Download Document

A
G.U.E.S.T.
course in
statistics
Bob Guest
Distinguished Lecturer
University of Tennessee
Mathematics Department
[email protected]
(those are zeros)
A G.U.E.S.T course in statistics is:
Guided
Understanding by
Experiencing
Statistics
Together
This Course is Under Construction
Math 115 Statistical Reasoning
A non calculus based general education
introductory statistics course
The Idea
• Student focused active learning course
(more than 50% of class time)
• Some instructor led discovery sprinkled in
• Strategic portions of the course flipped
Why Portable Populations?
Course objective #4)
Using the relationship between samples and
the populations they are taken from in
combination with the fact that when samples
are truly random they are also predictable to
calculate and apply sampling distributions to
various real world situations.
By having the students experiencing the
examples instead of just reading them, they
are developing a sense of intuition about the
subject as well as formulating their own
questions in real time as we carry out the
experiment.
This allows them to connect their thoughts
and understanding to their experience rather
than having to contemplate abstract
situations in their mind.
This results in a deeper understanding of the
concepts allowing students to learn to solve
problems rather than simply memorize
routines for coming up with solutions to
problems.
Examples of Portable
Populations
• 5000 random Scrabble tiles
Used to create customized populations
• 25 decks of Uno Cards
Used to create customized populations
• “Monopoly” and “Vegas” dice
Why use these?
Scrabble tiles and Uno cards
• Durable
• Light Weight
• Quantitative data and Categorical data
Why use these?
“Monopoly” and “Vegas” dice
• Durable
• Light Weight
• Quantitative data and Categorical data
• Challenge assumptions of fairness
Examples of Populations
Blue
Green
Yellow
Red
Mega
Deck
#0
2
4
0
3
#1
3
8
8
3
#2
5
8
8
3
#3
7
3
8
3
#4
8
1
8
4
#5
8
1
8
4
#6
7
3
0
8
#7
5
6
0
8
#8
3
8
0
8
#9
2
8
0
6
TOTALS
50
50
40
50
9
22
24
21
21
21
18
19
19
16
190
Symmetric
Bimodal
Uniform
Skewed left
Examples of Activities
Basic probability using the “mega deck”
If ONE card is randomly selected from a newly shuffled deck find these probabilities:
A) It is a 4?
B) It is a 5 given it is blue?
C) It is red and is a 7?
D) If one card is chosen and you see that it is a yellow card, what is the probability that
the card is a 9?
E) It is a 6 or is green?
F) If Four different cards are dealt at random without replacement, what is the
probability that they are all yellow?
G) If 150 different cards are dealt at random without replacement, what is the probability
that there will be at least one blue card dealt?
Examples of Activities
Using the Blue (symmetric), Green (Bimodal), Yellow
(Uniform) and Red (Skewed left) decks.
Calculate the discrete population mean, variance and
standard deviation for each color and graph each
population
Examples of Activities
Using the Blue (symmetric), Green (Bimodal), Yellow
(Uniform) and Red (Skewed left) decks.
Transform ( x  c and cx ) these populations to find the
impact on the mean, variance, standard deviation and
distribution leading to…
x

having a mean of 0 and standard deviation of 1
Examples of Activities
Another set of exercises leads students to discover:
2


2
X    X 
and  
X
n
n
so...
X 
X
X
 X 

n
has a mean of 0 and standard deviation of 1
Examples of Activities
Using the Blue (symmetric), Green (Bimodal), Yellow
(Uniform) and Red (Skewed left) decks.
Each student collects a sample of size n = 10, 25 and 50
from each deck (used multiple times in the semester)
Basic sample statistics calculated, then later confidence
intervals are calculated and hypothesis tests are done.
Examples of Activities
The results from all students are consolidated and used
to demonstrate:
1) The random nature of sample statistics
2) Sampling distributions
3) Compare statistical results to KNOWN population
parameters.
Semester project
There is a large population of Scrabble tiles and one of
Uno cards
1) The students collect data from these populations
2) They use the tools they have developed to draw
conclusions about these UNKNOWN populations.